NEW YORK (CNN) -- New York Mayor Michael Bloomberg announced Thursday he is asking the city council to change the office's two-term limit to allow him to run for a third term.

"If the City Council should vote to amend term limits, I plan to ask New Yorkers to look at my record of independent leadership and then decide if I've earned another term," Bloomberg said in a news conference at City Hall.

The mayor, a billionaire businessman, is credited with helping New York City recover economically after the terror attacks on September 11, 2001, which felled the twin towers of the World Trade Center and killed more than 2,700 people.

Elected for the first time just two months after the attacks, Bloomberg pumped tens of millions of dollars of his own money into that campaign, as well as his bid for re-election in 2005.

"As a businessman with expertise on Wall Street and finance and as a mayor who has balanced budgets and delivered services, I can tell you that the enormity of the challenges ahead should not be underestimated," Bloomberg said. "I care deeply about sustaining the progress we made and finishing the job the voters elected me to do." Watch Bloomberg talk about seeking a third term »

New York City Comptroller William C. Thompson, Jr., a Democrat considered a leading candidate to replace Bloomberg in next year's election, said he was "extremely disappointed" in the mayor's announcement.

"I have always taken the Mayor at his word, particularly when he said on multiple occasions that altering term limits through a council vote would be disgraceful," he said. "Let me be clear: Today's announcement constitutes an attempt to suspend democracy. We should not undermine the will of the voters."

Bloomberg, an independent since 2007, wants city council to change the current two-term limit law and offer voters another choice.

"As always, it will be up to the people to decide, not me," he said.

Standing beside Bloomberg at a later news conference regarding rebuilding at the World Trade Center site, New York Gov. David Paterson said he'd "be delighted to see [Bloomberg] running for a third term."

The mayor then jokingly pledged that he would not seek a fourth.

In 2005, Bloomberg easily defeated his Democratic opponent, Fernando Ferrer, the former Bronx borough president, who was never able to gain any traction against the popular incumbent.

Before becoming mayor, Bloomberg ran Bloomberg L.P., a global communications company that provides news and financial services to thousands of businesses worldwide.